KASHYK: It seems you have a long-standing obsession with exploration, Captain. I, on the other hand, have much more in common with this ancient soldier.
JANEWAY: He's from Earth's classical period. It produced some of our greatest artists as well.

Though I might be wrong, I'd have to get the dvd out. But none the wiser as to who it is

Actually google provides some images of antique Odysseus heads and there is some resemblance to Janeways bronze warrior head.
And for the too round cap: maybe Janeway patted it very often - for comfort. The shiny surface is an indication

"O Muse, tell of
The woman diverse in wisdom,
And much, in her life, with sorrow.
She helped, with her might, to have the Array fall,
The Caretaker's Array with its meaning, Array seen sadly by destiny.
His divinely built wall stood no more.
This woman wandered from planet to planet,
Observing as she went from place to place.
The ways of men and aliens she noted, how their lives were.
Oh, the spaces in tumult that she contested were innumerable,
And the ground beans, well roasted, she drank were countless."